The 2-D inplane displacement and strain calculation problem through digital image processing methods has been studied extensively in the last three decades. Out of the various algorithms developed, the Newton-Raphson partial differential correction method is the best performing quality-wise and most widely used in practical applications despite its higher computational cost. The work presented in this paper improves the original algorithm by including adaptive spatial regularization in the minimization process used to obtain the motion data. Results indicate improvements in the strain accuracy for both small and large strains. The improvements become even more significant when employing small displacement and strain window sizes making the new method highly suitable for situations where the underlying strain data presents both slow and fast spatial variations or contains highly localized discontinuities.

Digital image correlation (DIC) has been acknowledged and widely used in recent years in the field of experimental mechanics as a contactless method for determining full field displacements and strains. Even though several sub-pixel motion estimation algorithms have been proposed in the literature, little is known about their accuracy and limitations in reproducing complex underlying motion fields occurring in real mechanical tests. This paper presents a new method for evaluating sub-pixel motion estimation algorithms using ground truth speckle images that are realistically warped using artificial motion fields that were obtained following two distinct approaches: in the first, the horizontal and vertical displacement fields are created according to theoretical formulas for the given type of experiment while the second approach constructs the displacements through radial basis function interpolation starting from real DIC results. The method is applied in the evaluation of five DIC algorithms with results indicating that the gradient-based DIC methods generally have a quality advantage when using small sized blocks and are a better choice for calculating very small displacements and strains. The Newton-Raphson is the overall best performing method with a notable quality advantage when large block sizes are employed and in experiments where large strain fields are of interest.

Digital image correlation (DIC) has become a well-established approach for the calculation of full-field displacement and strains within the field of experimental mechanics. Since their introduction, DIC methods have been relying on only two images to measure the displacements and strains that materials undergo under load. It can be foreseen that the use of additional image information for the calculus of displacements and strains, although computationally more expensive, can positively impact DIC method accuracy under both ideal and challenging experimental conditions. Such accuracy improvements are especially important when measuring very small deformations, which still constitutes a great challenge: small displacements and strains translate into equally small digital image intensity changes on the material's surface, which are affected by the digitization processes of the imaging hardware and by other image acquisition effects such as image noise. This paper proposes a new three-frame Newton-Raphson DIC method and evaluates it from the standpoints of accuracy and speed. The method models the deformations that are to be measured under the assumption that the deformation occurs at approximately the same rate between each two consecutive images in the three image sequences that are employed. The aim is to investigate how the use of image data from more than two images impacts accuracy and what is the effect on the computational speed. The proposed method is compared with the classic two-frame Newton-Raphson method in three experiments. Two experiments rely on numerically deformed images that simulate heterogeneous deformations. The third experiment uses images from a real deformation experiment. Results indicate that although it is computationally more demanding, the three-frame method significantly improves displacement and strain accuracy and is less sensitive to image noise.

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